Final Report of CompMon Activity 4.4: Inversion Tool

Transcription

1 Final Report of CompMon Activity 4.4: Inversion Tool Milestone 15: Data form the Inversion tool validated Ari Karppinen Jari Härkönen Juha Nikmo Kari Riikonen Jukka-Pekka Jalkanen Lasse Johansson Finnish Metoeorological Institute 1

2 Contents Nomenclature 4 1 Introduction 4 2 Materials and methods Meteorological conditions : general Open Water Ice cover and transition region Weather conditions during the test periods Metorology during the intensive inversion test Time series of meteorological, emission and concentration data Overview of the airborne concentration measurements Emission estimates Dispersion model Results 13 3 Further development Gaussian modelling approach Modelling procedure Analytical Gaussian solutions with dry deposition and settling Continuous Gaussian plume versus Gaussian puff Results Observed and computed spectrum Computed vs observed mean concentrations Performance of the model Influence of plume rise on the performance of the model Estimation of emission rate of the source and plume rise from short period concentrations Conclusions from the second dispersion modelling study 28 4 Determining Ship Position and Velocity, Emission Strength and Plume Rise 29 2

3 4.1 Diffusion of a moving source emissions observed by a moving or stationary monitor Covering equations of the system Concentration spectrum Optimization procedure for ship location and velocity Optimization procedure for emission strength and plume height Remarks on the optimization procedures Computed results Utö test 34 5 Conclusions 38 Appendix A. Apparent and true wind 44 3

4 Nomenclature C = concentration (kg m -3 ) q = source strength (kg s -1 ) t = time (s) TL = Langrangian time scale (s) u = wind speed (m s -1 ) vs = speed (m s -1 ) wa = apparent wind speed (m s -1 ) y = crosswind distance (m) z = height above ground (m) Greek symbols, = angle (degrees) v, w = standard deviation of lateral and vertical wind fluctuations (m s -1 ) y, z = lateral and vertical dispersion parameters (m) 1 Introduction Present a simple Gaussian plume model for evaluating the dispersion of effluents originated from ships Compare the model predictions against an experimental dataset. Dataset measured at the island of Utö, Turku, Finland Other ship plume -models: o Gaussian plume: Frick and Hoppel (2000); Song et al. (2003) o LES model: Liu et al. (2000) o photochemical box model: von Glasow et al. (2003) 4

5 2 Materials and methods 2.1 Meteorological conditions : general Meteorology over the northern Baltic Sea surface changes seasonally between open water and ice cover and their mixture called transition region by Brümmer et al., Also the northern parts of the sea remain open the most of the year. Vihma and Haapala (2009) describe the general trends and statistics of the sea ice conditions of the northern Baltic Sea. Because the yearly, annual and spatial variation of the conditions over the Baltic Sea is great, a wider view is well grounded. During onshore flow the wind is from open sea to land. Similarly during on-ice wind the flow is from open sea to the fast ice and off-ice is the reverse. Both coastal areas and the ice edge regions induce mesoscale effects as sea breeze and low level jets. Their influence on pollutant dispersion is based on rapid changes in wind speed, stability and roughness length. The land-sea interface has the greatest impact to the flows over coastal areas. When the sea is open and cold i.e. in spring and during the first summer months, warm air flow from Estonian coast makes the stratification on coastal line of Helsinki stable and the roughness length very small (Mahrt et al., 2001). On the other hand, the unstable stratification over the open sea increases the roughness length. The influence of archipelago is a mixture of onshore and offshore effects. As a net effect advection of mechanically generated turbulence over the isles dominates spatially a few kilometers also over the sea increasing local mixing. If the air over isles is warmer than sea surface, a reduction of mixing is expected (Mahrt et al., 2001). The atmospheric stratification over the sea surface in archipelago is strongly seasonally dependent, but clearly in a more complex way as in case of onshore winds of a mainly plain shoreline. For example, the influence of archipelago of Turku is strong enough to break the sea breeze cell, which is present in front of Helsinki through the summer (Savijärvi et al., 2005) Open Water Atmospheric mixing conditions of MABL differ greatly from the corresponding situation over the land surface. This must be accounted, when the dispersion of ship emissions are computed during onshore winds at receptor points on the coastal line. 5

6 According to most researchers the Monin-Obukhov Similarity Theory (MOST) conditions are fulfilled rather well over the sea surface layer (SL). Carlsson et al. (2010) limits MOST only for conditions, when swell does not dominate and emphasizes problems if the atmosphere over the sea surface is close to neutral (2008). This is an implication of the sea spray to the sensible-heat flux (Larsén et al., 2004). Observations suggest different parameter values for stable and unstable statifications over the sea surface (Högström et al., 2008) compared to the use over land surface. The circulation in the Gulf of Finland is widely studied by monitoring and modeling and several mesoscale effects have been reported. According to Suhhova et al. (2015) upwelling at the Estonian coast is a coupled with downwelling at the Finnish coast changing the surface temperature (and stability), which further changes the drag coefficient of the air (Elken et al., 2011) and also the roughness length, which is usually determined according the formula by Garratt (1992) Ice cover and transition region The three weeks field measurement campaign BASIN over the Bothnian Bay 16Feb-06Mar in1998 included two coastal monitoring stations Umeå (Sweden) and Kokkola(Finland), marine research ship R/V Aranda and research aircraft Falcon (Brümmer et al., 2002, Vihma and Brümmer, 2002). Continuous spatial and temporal distributions of surface fluxes, roughness length stability and other meteorological parameters were monitored over the area 200 x 100 km including open water, transition region and ice cover. The high resolution results of the campaign form the basis of the winter time conditions are applied and are shortly reviewed in this work. Energy fluxes over the ice surface are more sensitive to the cloud cover than the open sea (Brümmer et al., 2002). Negative sensible heat fluxes over the ice surface associate with warm fronts and positive with cold fronts, which influence directly on stability. The mean values of both sensible and latent heat fluxes over the ice cover were positive due to conduction heat through the ice (Vihma and Brümmer, 2002). There is also a good correlation between the greatly varying albedo and the surface temperature of the ice cover. The variation of roughness lengths between coastal stations and M/R Aranda are crucial for the dispersion approach. The roughness length incorporates with the diabatic effect i.e. MOST is assumed over the ice surface. The smoothed values of roughness length over the ice varies 5ˑ10-5 m to 5ˑ10-3 m, while at the costal stations the values increase and especially variance changes according to 6

7 prevailing wind direction several orders: in Kokkola from 10-4 m to 10-1 m and in Umeå 10-4 m to 1 m. The results of Umeå may represent the seasonal situation generally in archipelagos, where the roughness length becomes locally very sensitive to the wind direction. Andreas (2011a, b) suggested a formula for the dependence of roughness length on friction velocity and kinematic viscosity over the snow coved ice surface Weather conditions during the test periods Meteorological measurements (wind speed and direction, air temperature and pressure) were carried out at the island of Utö ( N, E, WGS 84; see 0) at the height of 31 m above the mean sea level. Height of the mixing layer was estimated based on lidar (light detection and ranging) measurements. Atmospheric stability in terms of the Monin-Obukhov length (L) was determined applying measurements of sensible heat and turbulent momentum fluxes. Temporal resolution of the weather data measurements ranged from one minute to one hour. Measurements indicated that the atmospheric stability varied from extremely unstable (L m -1 ) to very stable (L m -1 ) conditions (0). Wind speeds at the height of 31 m above the sea level ranged from no wind up to approximately 23 m s -1 (0). The lidar based mixing height ranged from 35 m to 524 m. Temperature of air varied between -14 ºC and +11 ºC during the measurement campaign. Figure 1. Measured wind speeds at the height of 31m above sea level against the inverse of Monin-Obukhov length (L -1 ) at the island of Utö, Finland. The black and blue solid vertical lines at L 1 =0.1 m -1 roughly delineate the very stable and unstable atmospheric conditions. 7

8 2.1.4 Metorology during the intensive inversion test The sea was open during the period 26 Jan 31 Mar 2016 at UAMRS. Roughness length of the sea surface was predicted by the weather forecasting model HARMONIE with 3x3 km grid based on procedure by Garratt (1992). The comparison between meteorological parameters at Utö and HARMONIE forecasting model shows a good agreement except in case of MABL height. MABL heights by lidar observations were significantly lower than corresponding predictions. The reasons for differences are still uncertain and the forecasted MABL values are used in this test mainly due to a large number of missing observations in misty conditions. However, inversion layers below predicted MABL are highly probable, but their identified height is needed before applying to dispersion models. The distributions of meteorological parameters affecting on dispersion computations (figure 2) are presented in mathematical coordinate system (0 deg == E, 90 deg == N). The test includes even strong winds. Wind direction is mainly from the SE-NW sector, when the monitor is in the lee to the main ship channels. A few concentration signals were detected during eastern and northern winds. Stability (inverse of the Monin- Obukhov legth L) over the open sea surface was mostly near neutral, but also many unstable cases were determined during the test period. The ambient temperature (C) varies between The distributions of measured stability and forecasted MABL height are consistent. Inversion layer heights is not included in the test. 8

9 Figure 2. Distributions of meteorological parameters at UAMRS. Number of cases N in the test is 131 from the period 26Jan Mar Time series of meteorological, emission and concentration data Ships with stack height above 15 m are included in the test limits the number of cases N=131. Monitored meteorological and HARMONIE forecasting are combined into a time series of 15 min period. The period of ship position and emission time series changes between 5-15 s with mean of 10 s. The averaging time of measured NOx concentrations was 10 s. All parameters (and missing values) are interpolated into final time series with 10 s interval. The threshold for identification of NOx signal from the monitored time series was stated to 10 db compared with the local NOx background. The values of meteorological and emission parameters as well as ship location and velocity were identified from the beginning to the end of NOx signal. The time corresponding to the maximum of observed NOx signal is of a special interest in the study. Usually duration of a signal is a few minutes. Consequently, each monitored case is presented as a matrix including vectors of time, NOx concentration, meteorological parameters, ship emission, 9

10 location and velocity with 10 s intervals. The future computation can be limited only to times of observed NOx signals. 2.2 Overview of the airborne concentration measurements A measurement campaign was conducted during 1-Nov Mar-2016 at the island of Utö near the archipelago of Turku, Finland (0). Airborne concentrations of CO2, SO2 and NOx were measured with a Horiba instrument until 25-Jan-2016 and with a TEI 42S analyzer (Thermo Environmental Instruments) thereafter. The instruments were located at N, E (WGS 84) at the height of 11.5 m above the sea level. Figure 3. Locations of the concentration measurement device (blue star) and weather instruments (red star) at the island of Utö near the archipelago of Turku, Finland. The courses of ships during the measurement campaign, and considered in the modelling of dispersion of ship emissions are shown in solid coloured lines. 2.3 Emission estimates A total of 149 individual ships during the measurement campaign were, according to the Automatic Identification System (AIS) messages, reported to pass the island Utö while sailing to or from the 10

11 port of Turku, Finland (0). Further, a pilot boat was operating near and around the island of Utö. The courses of the vessels (location, speed, heading at a given time) were provided by the AIS-system. The AIS-system enabled the positioning of a ship with a spatial resolution of typically a few tens of metres (Jalkanen et al., 2012). Emissions strengths of CO, CO2, EC, NOx, OC, SO4, SOx and ash (in terms of unit mass per unit time) of each vessel were estimated with the Ship Traffic Emissions Assessment Model (STEAM; Jalkanen et al., 2009 and 2012; Johansson et al., 2013). 2.4 Dispersion model Let us first consider the physics of contaminant dispersion (= transport and dilution) through air from a point source. The source may be stationary, i.e not moving relative to for instance some fixed point on earth, or source may be in motion relative to some fixed location on earths surface. As the contaminants from the source are released into the surrounding fluid (air), the main fluid dynamical property of air influencing the dispersion is the velocity field of air relative to the (moving or not) source. Therefore, while constructing a dispersion model for ship emissions or for a stationary industrial stack, the physics of dispersion has to be viewed from the perspective of the source. While navigating on the sea, two concepts of wind are often used: apparent and true wind (fields). Apparent wind (speed and direction) is the wind as seen, or measured from a ship. True wind is the wind measured from a fixed location on earth (e.g. from a weather station). Clearly, if the speed over ground (SOG) of the vessel is zero, apparent and true winds are equal. Apparent wind is the field which drives the pollutant dispersion from a moving emission source, such as a chimney of a ship. Song et al. (2003) refer to apparent wind as the effective or resultant wind speed,..., and direction. Mathematical relation between the apparent and true winds is presented in Appendix A. We describe the contaminant dispersion due to emissions from a chimney of a ship with a simple Gaussian point source model assuming total reflection at the ground or sea level. Further, the released material is assumed to be chemically inert and deposition processes (dry and wet) are neglected. Further, the assumptions inherent in Gaussian formalism apply: (1) the atmospheric conditions, such as wind velocity and air temperature, remain spatially and temporally constant, and (2) the source strength is temporally constant. Obviously, changes in vessel speed, its course (direction) and emission strength needs to be assessed when evaluating the validity of the model results. 11

12 For simplicity, the coordinate system has been chosen as follows. Its positive x-axis is in the direction of the mean apparent wind, y-axis is laterally perpendicular to the x-axis and z-axis in the vertical direction. The time-averaged concentration field C for a continuous, steady plume is of the form (Seinfeld, 1986) C = q 2πuσ y σ z exp ( y2 2σ y 2 ) [exp ( (z z e) 2 2σ z 2 ) + exp ( (z + z e) 2 2σ z 2 )], (1) where q is the source strength; u is the apparent wind speed; y and z are the lateral and vertical dispersion parameters, respectively; and ze is the release height above ground or sea level. The dispersion parameters are estimated by the formulas proposed by Draxler (1976) and Gryning et al. (1987) applied in a wide variety of models (e.g. Nikmo et al., 1999). The form of the parameters derive from the early work of Taylor (1922) (see e.g. Pasquill, 1971; Hanna et al., 1982; Draxler, 1976) σ y = σ v t f y (t T Ly ) (2) σ z = σ w t f z (t T Lz ) (3) where v and w are the standard deviations of lateral and vertical wind speed fluctuations, respectively; t is the travel time from the source; TLy and TLz are the Lagrangian time scales for crosswind and vertical dispersion, respectively; and fy and fz are functions of the Lagrangian time scales and the wind fluctuations. For details, the reader is referred to Nikmo et al. (1999). Plume rise in the near field has been ignored due to insufficient experimental data. Therefore, the release height (ze) was assumed to be equal to the top of the chimney of the vessel. The model is contructed as follows. Given the AIS-messages of a vessel (locations and time stamps of the messages), a straight line course between two consequtive messages is assumed. The speed and heading is obtained from the length and the end points of the line. For each line segment the (estimated) emission rate and the meteorological condition are assumed to remain constant. Dispersion estimates are then calculated applying Eq. (1) for each of the line segments. Eq. (1) 12

13 expresses the results in a coordinate system which is moving with (is fixed to) the vessel. A straigthforward coordinate conversion between moving coordinate systems is applied in order to calculate the concentration at an earth-fixed point (e.g. at a concentration measurement instrument). 2.5 Results Due to difficulties in processing the concentration measurements, only the period from 1-Feb-2016 to 31-Mar-2016 was considered. Only NOx emissions of the vessels are considered. Measured NOx concentrations are averaged over one minute. The measured NOx concentration indicated that the background concentration was roughly in the range of 2 g m -3-5 g m -3. Measured concentrations greater than 10 g m -3 were assumed to be originated from ship emissions. Examples of measured and modelled NOx airborne concentration, and estimated NOx emission of ships passing the island of Utö are shown in 4. Two observed and concentration peaks (due to ship emissions) can be identified, both of which are fairly well captured by the model. However, the model estimates an additional peak not shown in the measurement data. A total of 132 peaks were identified from the measurement data, while 164 peaks were estimated by the model. The average durations of an observed and modelled ship plume to pass the concentration instrument were 4.3 and 3.9 minutes, respectively. 13

14 Figure 4. Measured (blue line) and modelled (red line) NOx concentration, estimated NOx emission (green circles) of ships passing the island of Utö. The overall performance of the model (its success to predict concentration peaks due to ship emissions) was measured with hit rate. The hit rate (H) gives the relative number of times an event was forecast when it occurred (e.g. Stephenson, 2000) H = a a + c, (4) 14

15 where a is the number events which where both observed and modelled, and c is the number of events observed but not modelled. Clearly, a +c is the total number of observed concentration peaks. In order to determine a and c, we have defined three gauges (criterions) in terms of local concentration maximums (peaks) 1. a (observed and modelled) peak has at least a concentration of Cmin = 10 g m the temporal difference (defined to be >0 ) of observed and modelled peaks 3. the ratio of observed (Cobs) to modelled (Cmod) concentration peak ( max(cobs / Cmod; Cmod/ Cobs) Cratio) The criterion (1) attempts to distinguish a measured peak from the background concentration. Criterion (2) allows the observed and measured peaks to occur at different time instances (see e.g. 0) and criterion 3 controls the allowed relative difference in the heights of the peaks. The hit rate for a range of values of t and Cratio is illustrated in Figure 5. 15

16 Figure 5. Hit rate as a function of time difference between observed and modelled peaks and the relative difference of the peak heights The analyses seems to indicate that even a simple modeling approach can lead to acceptable hit-rates, but only if some relaxation in the exact timings and exact peak heights are allowed. While this analyses seems to indicate that assigning 5 minutes as the allowed error in timing and allowing peak ratios on the order of 3-5, would already lead to quite an acceptable, 50% hit ratio. Repeating this analyses with longer time series would give more reliable values for the parameters, but this analyses is already enough to show, that even the very simple modelling approach can be useful in practice, and further development work towards an inversion tool based on these simple dispersion modeling tools is thus fully justified. 3 Further development Gaussian modelling approach Here we describe and use a slightly refined gaussian plume formulation for the problem, with the aim of developing the local scale inversion tool based on this formulation. The used plume and puff models (Stockie, 2011) accounts also for dry deposition and settling. Differences between dispersions of puff and continuous source approach are expected to be quite insignificant when the distance increases and the continuous Gaussian point source model is applied to emissions of 10 s intervals. However, the theoretical correction factor (Palazzi, et al., 1982) between continuous and puff dispersion is applied to the puff estimate. 3.1 Modelling procedure There is a fundamental difference between the dispersion of stationary and moving emission sources. Dilution of the Gaussian plume from a stationary source is inversely related to the norm of wind vector u, but in case of moving sources we replace it by the norm of relative velocity u-v, where v is the velocity of the source. Relative velocity is also used in computation of dispersion parameters, when transportation time for distance D is D/ u-v. Plume axis is now in the direction of vector u-v and the direction is conserved, if wind and source velocities are constants. 16

17 The relative velocity u-v is also called the apparent velocity in literature. Figure 6 illustrates the dispersion of moving ship emissions. The monitor observes the maximum concentration, when the ship has moved to the position of Apparent Emission and transportation time is Di/ u-v. During this time ship travels the distance Di v / u-v. The monitor detects signal from the green colored zone of the ship channel, though emitted in the Actual Emission zone. u-v Monitor locates at rm Di Actual Emission Apparent Emission v Figure 6. Actual and apparent emissions regions of a ship channel. Wind and ship velocities are u and v, respectively. The monitor observes the maximum of the concentration signal at time t0. Duration of the signal is t2 t1 and spans discrete times [t1,,t0,,t2] with intervals t=ti-ti-1=10 s. At the same time ship locates at points [rs(t1),,rs(t0),,rs(t2)] in the apparent emission range. The point rs(t0) is read from the STEAM2 AIS data and rs(ti)=rs(t0)+v(ti-t0). Dot product Di= (rm-rs(ti)) (u-v)/ u-v yields the distance between the ship and monitor. Emission strength (g/s) and ship velocity is assumed constant during t2-t Analytical Gaussian solutions with dry deposition and settling Gaussian dispersion or diffusion from stagnant sources is widely treated in textbooks. The boundary value problem is solved by Green s functions or Laplace transforms e.g. Crank (1975), Seinfeld (1987), Stockie (2011). The solution of Fick s diffusion is normally called K-theory. The mutual dependence of the several parameters in use is firstly presented. Diffusion constants are Kx, Ky and 17

18 Kz in units m 2 s -1. Dispersion parameters in atmosphere are x, y and z in units m. Both Ki and i depend on travel time and diffusion becomes approximately Gaussian, but the vertical dependence is usually omitted in SL of the local scale. Also a widely used parameter r (m 2 ) associates with atmospheric dispersion according to equation (5c). K y = d y 2 2dt K z = d z 2 2dt if K y = K y (x), then y = 2 K y (x x s ) if K z = K y (x), then z = 2 K z (x x s ) u u (5a) (5b) r = 1 x u 0 K(x )dx if K = K(x), then r = 2 2 (5c) The principal difference between the modeling of ship and stagnant source emission is the short time period usually only a few minutes, when the signal from the plume from a ship is available at the monitor. Moreover, the relation between wind and ship velocity vectors determines the character of the plume. It may be approximately continuous or puff. Lin and Hildemann (1997) present stationary concentration C(x,y,z) in the generalized form (6) for continuous point and finite line sources. The factors Q and Gy of the product are explained in Table 1, while the concentration by unit length Cu(x,z) is presented separately in equation (7). C(x, y, z) = Q C u (x, z) G y (6) Source type Point source Finite line source Emission strength Q(units) Qp(kg s -1 ) QL(kg m -1 s -1 ) Cross-wind dispersion factor Gy(units) G y = 1 2 y exp [ (y y s )2 2 y 2 ] (m -1 ) (7a) G y = 1 [erf 2 (L s 2 y ) + erf ( L s 2+y )] (-) (7b) 2 y 2 y Table 1. Source type, emission strength Q and cross-wind dispersion factor Gy with corresponding dimensions according to Lin and Hildemann (1997). Length of the line source is Ls (m). 18

19 Stockie (2011) applies Ermak s equation to dry deposition and settling velocity, which is also followed in this work due to large size distribution of particulates of ship emissions. Concentration of unit strength Cu(x,z) (m 2 s -1 ) is for total reflection at air- sea interface (7c). Parameter w0 is defined by dry deposition velocity wdep(ms -1 ) and settling velocity wset(ms -1 ) according to w0 = wdep wset/2. Parameter zs = stack height + plume rise. C u (x, z) = 1 exp [ w set (z z s ) 2 u z 2K z {exp [ (z z s )2 2 2 ] + exp [ (z+z s )2 z 2 2 ] 2 w 0 z exp [ w 0 (z+z s ) z K z w set 2 2 z 8K2 ] (7c) z + w z K z 2K z 2 ] erfc [ z+z s + w 0 z ]} 2 z 2K z The influence of dry deposition and settling is greatest in lowest part of SL and increases with distance. Mixing conditions over the sea surface is crucial, which is the reason for the relatively wide attention to the MABL in this study. The uncertainty of inversion layer heights in this work is a potential error source of the results. Note that equations (5,7) describe dispersions from stationary sources. In case of moving source with velocity v the wind speed u is replaced by the norm u-v and the distance between the source and the monitor is determined in the direction of the vector u-v. 3.3 Continuous Gaussian plume versus Gaussian puff Continuous Gaussian plume is regarded as a superposition of overlapping Gaussian puffs, but not vice versa. Emission plumes by ships have line-type geometry, where radius increases by diffusion. Relative changes between wind and ship velocity vectors may produce puffs or nearly continuous plumes from the same ship at the monitor. Palazzi et al. (1982) suggested a correction factor fc(x, ) for a stationary source in eq. (7a), which transforms a continuous steady state solution (6) to a puff in equation (7b). This is important for discretized ship channels, where the release time r equals the discretization time. Horizontal dispersion parameters are assumed equal x(x) = y(x) and are directly available. Monitor locates at a distance x from the source and transport time is denoted by. Correction function is distributed over and the maximum is always at = r/2 + x/u. The function fc(x, ) stretches temporally with x, but conserves the mass. Again wind speed u in equations (5) is replaced by the norm u-v and the 19

20 distance between the source and the monitor is determined in the direction of the vector u-v for a moving source. fc(x, τ) = 1 [erf 2 (x u(τ τ r ) ) erf ( x uτ ) ] τ > τ 2 x 2 r x Puff concentration CP(x,yz, ) is a product of correction function (8a) and a steady state concentration (5) as shown in equation (8b). Consequently, also the puff concentration becomes distributed over time, when integration yields the total puff concentration. CP(x, y, z, ) = fc(x, )C(x, y, z) Integration of (48b) over ( r, ) reduces to integration of (8a) yielding always r. The result is important, since it combines the physically different emission strengths of continuous plume [Q]= kgs -1 and the total emission strength of puff [Qtot]=kg. It confirms that the mass is conserved in (8b) and produces the temporal distribution of observed concentration at the monitor. The distribution is fixed by location of maximum = r/2 + x/u and the earlier and after parts of it are mapped to the corresponding observation times. Deviation between the continuous and puff approaches become evident, when the distance between ship and monitor is only a few hundred meters. At greater distances simulated results are approximately similar. (8a) (8b) 3.4 Results A fixed monitor intersects the plume along the line, which is in direction of the vector v illustrated in figure 1. The observed concentration has one mode and the observed maximum locates on the axis of the plume. After detecting signal (>10 db) from the background the concentration signals still include error, which increases when averaging time decreases. Consequently, raw data may deviate considerably from the expected one mode distribution. Therefore raw data is filtered to yield the mean time dependent signal as in figure 9. Corrected observations are sampled from the filtered signal at times of the observed raw data. The prevailing weather parameters during the test were already presented in figure 1. Corresponding emission and mean concentration distributions are in figures 7 and 8. Figure 7 suggest two groups for ship speed as also for emission rate, which are correlated. Two peaks in ship heading is due to the direction of the main ship channel locating in NS direction. 20

21 Figure 7. Distributions of ship speed, heading and emission rate in the test (N=131). NOx concentration were computed by continuous point source model (eq. 3) denoted by ConDepo with dry and settling depositions were 0 ms -1. Plume rise is assumed zero by default.the puff concentration ConPuff at the monitor was estimated by eq. (4). Exposure using puff approach moves the weight to smaller concentrations. Filtered concentration (observation) distribution closely follows the corresponding ConDepo distribution. 21

22 Figure 8. Histograms of the mean continuous plume (ConDepo), puff (ConPuff) and filtered (Filtered) concentrations in the test (N=131). 3.5 Observed and computed spectrum The measured concentration spectra is symmetric only in case vector u-v is perpendicular to v. Otherwise they are skewed as in the example of figure 9. In this case the spectrum of exposure (ConPuff) is closer to the observed (Filtered) concentration compared to continuous plume estimate (ConDepo). The observation time (passage time) is about two minutes and the maximum locates at time 0 seconds. The variation between observed and predicted concentrations is large. 22

23 Figure 9. Continuous plume, puff and filtered concentrations at monitor against passage time. 3.6 Computed vs observed mean concentrations The comparison between computed and observed mean concentrations in figure 10a shows large scatter, which is typical in field experiments when measurements cannot be repeated in exactly same conditions. The bound lines represent the factor of two. The mean puff concentrations (ConPuff) are clearly underestimated compared to the mean observations (Filtered). The means of plume estimates (ConDepo) are more evenly distributed over the observation values. Recall that even with mean concentrations the averaging time is usually only a few minutes. Since the local impact on the environment is crucial, the mean values against passage time are presented in figure 10b. The exposure time at a fixed point is typically a few minutes and rather seldom the mean concentration 100 g m -3 is exceeded in wintertime conditions, when the distance from ship channel is more than one kilometer. The situation with smaller distances is unknown. The maximum concentrations during the passage are roughly 3 x mean concentration (figure 5). A few 23

24 large passage times (with low concentrations) obviously include concentrations from more than one ship. The means of the exposure time and NOx concentration are 306 s and 38 gm -3, respectively. 24

25 Figure 10. Scatterplot (upper panel) of estimated the mean plume (ConDepo) and puff (ConDepo) against the observed (Filtered) concentrations. The estimated and observed concentration against passage time are presented in the lower panel (N=131). 3.7 Performance of the model The scatterplot of figure 10 indicates large variation between estimates and observations. We can draw conclusions from estimated values in four ways using classification e.g. Martinez and Martinez (2008) in Ch. 10. The concept of Receptor Operating Characteristic (ROC) helps the decision making from the estimates in probabilistic scheme. It is widely used as performance test of a model in statistics and signal processing. The deviation between concentrations ConDepo Filtered obeys closely a t-distribution, from which the scale parameter sigma is computed. Defining success as estimated values between sigma and false the excluding cases produces a binary distribution for the threshold bounds. Logistic regression is appropriate for analyzing binary phenomena. The binary distribution is firstly fitted into logistic regression by the general linear model yielding probability estimates. Plotting true positive probability against false positive illustrates the ROC curve in figure 7 representing the probability to make correct decision from correct predictions (vertical axis) and correct decision from false prediction (horizontal axis). True positive rate represents the probability of correct classification, while false positive rate indicates incorrectly classified cases. The curve must be concave and above the 45 o line. The optimal operating point of the model is also denoted representing the best performance that can be achieved (e.g. Kay, 2013 in p. 202). The curve rises rapidly in case of a good model and then bends slowly towards one. The area under the curve (AUC) represents the performance of the model. According to Hosmer and Lemeshov, 1989 (p.162) the acceptable lower limit for the model is AUC=0.7, while AUC=0.5 represents the toss of coin (1:1 line in figure) and AUC > 0.8 for a good model. The performance of the continuous plume model is acceptable and consistent with the scatterplot in figure 6a. Accounting the demanding field test period the result for a local dispersion model is an encouraging trial for using time series with short averaging time. The low number of cases in the test limits further conclusions from the results. 25

26 Figure 11. The ROC of the model ConDepo, when succeeded prediction allows the deviation of prediction sigma from the filtered values. The deviations obeys a t-distribution. The area under the curve is AUC=0.739 and N= Influence of plume rise on the performance of the model Plume rise indicates the properties of exit gases, but also the properties of MABL as heights of inversion layers, wake effect and dry deposition during the transportation. If the Gaussian plume is accepted to describe dispersion in local scale, the changes in assumed plume rise should reflect to the performance of the model. Figures 10 and 11 illustrate the scattering of concentration and performance when plume rise is zero. Marelle et al. (2016) reports 60 m for the mean height of plume axis after a few hours of emission indicating positive plume rise. The measured plume axis is above the stack height due to a true plume rise or absorption on the surface indicating an apparent rise, while inversion layers, wake effect and dry deposition declines the plume axis height. 26

27 The influence of plume rise on the performance is simulated by two plume rise values 10 m. The result in figure 8 suggests that positive plume rise decreases and negative improves the performance. The difference between the performances is significant. Consequently, inversion layers, wake effect and dry deposition obviously influenced on the dispersion and predicted NOx concentrations in the test. Figure 12. The ROCs computed with plume rise +10 m (left panel) and -10 m (right panel). The corresponding AUC values are and N= Estimation of emission rate of the source and plume rise from short period concentrations Since each case includes a few tens of predicted concentrations, the least squares fitting procedure using eq. (7) can be applied to separate cases in determining their emission ratio and plume rise. The procedure is validated in figure 13, where the estimated emission rate by the fitting procedure equals the corresponding STEAM2 emission rate with high correlation. The input plume rise was assumed 27

28 zero, which is also returned by the fitting procedure. The applied method corresponds well the overall expectations. Figure 13. The validation of the least squares method for estimating emission ratio and plume rise from predicted concentration time series in 131 cases. Measured concentration time series with short averaging period offers a chance to estimate emission rate from concentration spectra. This requires the implementation of a satisfactory dispersion model to the fitting procedure Conclusions from the second dispersion modelling study NOx concentrations by ship emissions were measured and predicted during 26Jan Mar2016 at Utö Atmospheric and Marine Research Station (59 o 46 50N, 21 o 22 23E) in the Baltic Sea. Gaussian plume and puff models were tested against filtered observations using 10 s time interval in 131 separate cases. Large variation between estimates and observation was found both in case of 10 s averages and total signal means, which is typical for field tests. Exposure time at the monitor is usually a few minutes, when the concentration is normally below 100 gm -3. The means of the exposure time and corresponding NOx concentration are 306 s and 38 gm -3, respectively. The performance of the Gaussian test model is reasonable. The results suggests that inversion layers, wake effect and deposition are potential indicators of the large scattering between modelled and observed NOx concentrations. 28

29 Measured concentration time series with short averaging period enables the estimation of emission ratio from the measured concentration time series assuming that satisfactory dispersion model is available. 4 Determining Ship Position and Velocity, Emission Strength and Plume Rise The reverse approach e.g solving of the inverse problem, where a short period (10 s) time series of NOx concentration and meteorological data are applied to assess ship position and velocity. The solution of the inverse problem is classical i.e. the search of single values of the unknowns by optimization instead of determining their probability distributions as in case of the Bayesian approach. The results can be further utilized in estimating ship emission strength and plume height at the monitor from the Gaussian plume equation as in Part I completing the solution for the inverse problem. The solution is applicable both for a stationary and a moving monitor with constant velocity. As before, the emission strength estimates are based on STEAM2 model, described by Jalkanen et al and compared with measurements e.g. by Marelle et al. 2016, are used as a reference values in the current work. The objective of this work is to study possibilities to develop a method for assessing emission strength, plume rise and ship position and velocity from the measured concentration time series in local scale. The inverse problem is solved in the classical sense, when single values of the unknown ship position and velocity are estimated by a nonlinear, constrained optimization procedure applied to meteorological data. After this LSQ fitting is applied to the observed time series of concentration yielding emission strength and plume height estimates. The Gaussian plume equation is utilized in the dispersion process for both stationary and moving sources. 4.1 Diffusion of a moving source emissions observed by a moving or stationary monitor The conventional Gaussian plume equation for a fixed source is transformed to a moving source by replacing the norm of wind velocity u by the norm of relative velocity u vs, where vs is the ship velocity vector. Consequently, emissions transport with the speed u vs in direction of vector u vs. Atmospheric diffusion of the Gaussian plume affects only in the plane perpendicular to vector u vs. If also the monitor moves with velocity vm, its relative velocity against the ship is vm-vs. The situation is illustrated in figure 1, where monitor s initial position is rm0 and it arrives to the boundary of the 29

30 plume at the point r1. The monitor observes the axis of the plume at point r0 and the last observation is at r2. The position of ship is rs. Due to the ship velocity vs, the monitor intersects the plume along the section line (SL) in direction of vector vm-vs. If the monitor is fixed (vm=0), the intersection is in direction vs. The monitor maps time and location continuously. The optimization procedure of ship position and velocity is based on figure 15, when only the lateral part of the Gaussian plume equation is needed. The solved parameters are used further in optimization of source strength and plume height from the whole plume equation. The direction of the plume axis keeps unchanged, though the position of the plume changes. u-vs rm0 vm-vs SL r2(ts2) r0(ts0) r1(ts1)=rm0 + vm ts1 GL vm rs(ts0) vs Figure 15. The monitor arrives from the right (bold) with velocity vm, observes the boundaries of the plume at r1 and r2 and plume axis at r0. The ship at rs moves with velocity vs. Wind velocity is u. 4.2 Covering equations of the system Equations are presented in right handed coordinate system, where xw is along the plume axis (in direction of u-vs) and yw is perpendicular to it. Origo locates at ship position rs. The section line SL intersects plume axis at xw0= r0-rs. Perpendicular distance from the axis is yw in eq.(1), where k is the slope 30

31 yw = k (xw xw 0 ) (9) The Gaussian plume (total reflection assumed) is factored into three parts in eqs. (10). Parameter Q is emission strength (g/s), lateral and vertical dispersion parameters are y and z, monitoring height is z and height of the plume axis h (both a.s.l.). C(xw, yw, z) = f 1 (xw) f 2 (xw)*f 3 (xw), where (10a) f 1 (xw) = Q 2 π σ y (xw) σ z (xw) u v S (10b) f 2 (xw) = exp ( 0.5 ( yw(xw) 2 ) ) (10c) σ y (xw) f 3 (xw) = exp ( 0.5 ( z h σ z (xw) )2 ) + exp ( 0.5 ( z+h σ z (xw) )2 ) (10d) On the plume axis yw(xw)=0, when f2(xw)=1 according to (2c). This indicates that by dividing the measured concentration spectra by its maximum, we may expect the resulting distribution to follow also eq. (2c). This is because monitor observations are collected always on SL line. Also we can assume that with probability > 0.99 the observed values come from -3 y(xw) yw(xw) +3 y(xw). Determination of stability and the dispersion parameters y and z is based on the MOST procedure. 4.3 Concentration spectrum The raw data is erroneous by default including monitoring errors and physical uncertainties during the transportation from source to monitor. Averaging period of concentration is 10 s. The typical observing time of monitor is from tens of seconds to a few minutes in local scale. Because the mathematical form of the concentration distribution is still unknown, fitting cannot be considered. The average spectrum from the raw data is produced by a two phase filter. The filter is helped by interpolating a great number of random query points between observed values. Window size is determined to produce a one mode distribution, which is physically adequate for the Gaussian plume. A real filtering example :38:20 is shown in figure 2. After removing the background concentration query points (green line) were interpolated between observed values (raw obs), which are interpreted as true values by the filter. The filtered result (filtered) is hereafter the input signal, 31

32 whose discrete values are sampled at raw data times. The input data to the optimization procedure includes the sampled discrete values. Division the spectrum by its maximum produces the empirical signal comparable with equation (2c). Figure 16. The probable signal is the filtered line (see text) from which discrete values are sampled at raw observation times. The maximum of the signal is monitored :38: Optimization procedure for ship location and velocity Nonlinear, constrained local optimization procedure fmincon is applied to input data. Algorithms sqp and interior-point are used. Three unknown variables is needed: x(1)=transportation time from ship to monitor (s) x(2)=ship speed (m/s) x(3)=ship heading (rad) The functions in the text are defined in Apendix. As earlier mentioned, the observed data (ydata) is the filtered signal divided by its maximum value. We can apply equation (10c) to g2(x) as defined in 32

33 Appendix. The scaled difference between model and observation is G(x) in Appendix, whose norm is the objective function being minimized Objective function = G(x) (11a) Three variables allows the use of two equality constraints ceq and unlimited number of inequality constraints c, which are defined in Appendix. The 1 st row of ceq: u-vs = sum of projections of vm-vs and u on the plume axis. The 2 nd row in ceq is used only in testing the procedure with known distance D between ship and monitor using STEAM2 data, see Results. The inequality constraint c states yw-values between [-3 y(xw), +3 y(xw)]. The minimization problem is Subject to ceq = 0 with bounds min x G(x) (11b) c 0 x low x x up The distance between ship and monitor is d= x(1)*uv(x). When distance d, the unit vector euv(x) and location of monitor rm are known, an estimate to ship location is rs = rm-x(1)uv(x)euv(x). The monitor locates within the plume during the time period dt*in1, where dt=10 s and in1 is the corresponding vector of indices. 4.5 Optimization procedure for emission strength and plume height When u-vs and y(x) and z(x) are determined, eqs. (2) are used in estimation of emission strength Q (2b) and plume axis height h (2d). The optimization problem is actually a least squares fitting procedure, where observed data is now the discrete filtered data and predictions come from equation (2a). 4.6 Remarks on the optimization procedures The solutions by algorithms sqp and interior-point are equal in average, but they may fail in different cases. The combination of both algorithms increases the number of success about 30 %. Using one stationary monitor accepts ship headings and + due to the geometry, because slope values k(x) and k(x) produce the same solution. This is the case in Utö project and only a limited 33

34 comparison can be done. Estimation of emission strength and plume height is possible, when AIS data by STEAM2 is used for determining ship location and velocity. If instead of stationary, we have a moving monitor, we can repeat the trial by changing the slope of SL. From these trials the true direction is concluded, which is outside this test. 4.7 Computed results The total number of cases N=135, when stack height of ships 15 m. Without any limitations third part of optimization trials fails. As earlier mentioned, we have only one monitor and Utö test is limited for comparison of estimated emission strength (by this model) with that predicted by STEAM2. In case of plume height, we have no reference. However, a qualitative assessment of plume rise (= plume height stack height) against distance can be done. 4.8 Utö test Limitations and bounds: 1. The 2 nd row of ceq is in use, where D= distance between ship location (STEAM2) and monitor 2. Ship speed x(2)= ShipSpd(STEAM2) 2 m/s 3. Ship heading x(3)= ShipDir(STEAM2) 30 o Less freedom for optimizer is available and if the atmospheric diffusion process is not Gaussian, the optimizer may fail. The number of fails increases to 51 %. This is also expected by the large deviation between observed and estimated MABL heights in Utö. Considerable overestimation is observed, while on the basis of the work by Marelle et al the reverse behavior is expected. The result indicates the existence of low inversion layers, which is not accounted by the current model. The overall performance of the algorithms is rather similar in figure

35 Figure 17. Comparison of algorithms sqp and interior-point. Number of cases is 66 out of 135. Estimate of emission strength against the corresponding STEAM estimate is in figure 4. Considerable overestimation is found. The cases (25) within factor of 2 (FAC2) are circled. 35

36 Figure 18. Emission strength by STEAM2 against the estimate of this model is plotted. Number of All cases is 66, while number of cases Within FAC2 is 25. Estimated plume rise = estimated plume height stack height is presented in figure 19. Plume height was limited between stack and MABL heights. Now the circled plume rise values refer to Figure 18 i.e. they represent plume rises, when corresponding emission strength is within FAC2. There are three unreasonably high values, while most of them are within reasonable limits. 36

37 Figure 19. Plume rise against distance. Number of All cases is 66 and Within FAC2 25. The trade-off between emission strength and plume rise is studied by limiting the upper limit of plume rise to 100 m. As a result the number of success is 69 and number of cases within FAC2 is 25. The distribution of emission strength is practically unchanged in figure 20. Figure 20. The influence of plume rise limited to 100 m on emission strength, NAll=69, NFAC2=25. 37

38 5 Conclusions A study for determining ship location and velocity, emission strength and plume rise from the measured concentration timeseries at Utö Marine Research Station is presented including theoretical basis and a several different solution methods in local scale. The data is also used for directly evaluating the inverted emission against corresponding values estimated by the STEAM2 model. One clear conclusions is, that all the tested inversion methods perform satisfactorily, if the meteorological conditions are well/perfectly known. However, it was observed, that quite often some crucial meteorological information was very uncertain so at the end the performance of the evaluated methodologies were at most satisfactory during winter conditions Several improvements, which would clearly enhance the reliability of the inversion are suggested. The procedure will offers a reasonable choice for the assessment of emission strength and plume height from measured concentration time series on locations where supporting tracer measurements (CO2) are not available. One of the main problems identified in our study was the difficulty of determining reliably the height of mixed layer of inversion layer. The ongoing monitoring project at Utö will l help to solve the problem but in our study it was clearly observed that the agreement between onsite lidar observations and NWP-forecasted MABL are unsatisfactory. Also it was clearly found out that, implementing the plume height model (accounting inversion layers) to the dispersion treatment is necessary. 38

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44 Appendix A. Apparent and true wind Definitions: true wind speed is the speed of air particles measured from, or at, a stationary point relative earth (e.g. at meteorological measurement station) true wind direction is the direction of air particles measured from, or at, a stationary point relative earth apparent wind (its speed and direction) is the wind experienced by, i.e. measured from, objects moving relative to earth Applying basic physics and geometry (see Fig. A1), apparent wind speed (wa) is given in terms of true wind speed (u), object speed (vs) and the angle between their directions ( ) by w a = (u 2 + v 2 s + 2uv s cos(α)) 1 2, (A1) where is the angle (direction of movement) of the object relative to the true wind direction ( = 0 for upwind; = 180 for downwind). The angle of apparent wind ( ) is (see Fig. A1) β = arccos((u cos(α) + v s )w a 1 ). (A2) Fig. A1. Relation between true (u ) and apparent (w ) a wind velocities for a moving object. Notation: vs = speed over ground of the object, = angle of true wind, = angle of apparent wind. 44